1. The problem statement, all variables and given/known data
Convert the decimal number 2000.90210 to a single-precision IEEE 754 hexadecimal.

2. Relevant equations
(exponent field)_10 - 127_10 = exponent_10
The first bit is the sign bit.
The 2nd to 9th bits are the exponent bits.
The 10th to 32nd bits are the fraction field bits.
1.(fraction field)_2 x 2^(exponent_10) leads to the base 10 final answer

3. The attempt at a solution
My attempt at the solution is attached as MyWork.jpg.

I was planning to convert it to the binary IEEE 754 32-bit single-precision representation since that's what I am familiar with and then convert it to hexadecimal however, it seems that when I do this, my binary version is far off from the decimal value I'm initially given.

I'm not sure but, this might be related to the fact that the binary fraction field is (at least, seemingly) irrational.

Staff: Mentor

I'm not sure but, this might be related to the fact that the binary fraction field is (at least, seemingly) irrational.

Rational <-> irrational is independent of the base you express a number in. There is no exact representation of the number with a finite number in base 2, but that does not matter. It just gives a small rounding error.

my binary version is far off from the decimal value I'm initially given.

Rational <-> irrational is independent of the base you express a number in. There is no exact representation of the number with a finite number in base 2, but that does not matter. It just gives a small rounding error.

Alright.

In which way?
Your attempt looks fine.

When I input my binary IEEE 754 answer to this ( http://www.h-schmidt.net/FloatConverter/IEEE754.html ) website, the decimal representation is around 4001.80. If it's not my work that's wrong, what's wrong with the Java applet software or with the way I am “communicating” with it?

Staff: Mentor

When I input my binary IEEE 754 answer to this ( http://www.h-schmidt.net/FloatConverter/IEEE754.html ) website, the decimal representation is around 4001.80. If it's not my work that's wrong, what's wrong with the Java applet software or with the way I am “communicating” with it?

I would not call this "far off", it is exactly a factor of 2, indicating a problem with the exponent. rcgldr found the error.